diff --git a/README.md b/README.md
index a39da242e..dc99cc7b5 100644
--- a/README.md
+++ b/README.md
@@ -31,6 +31,7 @@
 - Vanilla Imitation Learning
 - [Batch-Constrained deep Q-Learning (BCQ)](https://arxiv.org/pdf/1812.02900.pdf)
 - [Conservative Q-Learning (CQL)](https://arxiv.org/pdf/2006.04779.pdf)
+- [Twin Delayed DDPG with Behavior Cloning (TD3+BC)](https://arxiv.org/pdf/2106.06860.pdf)
 - [Discrete Batch-Constrained deep Q-Learning (BCQ-Discrete)](https://arxiv.org/pdf/1910.01708.pdf)
 - [Discrete Conservative Q-Learning (CQL-Discrete)](https://arxiv.org/pdf/2006.04779.pdf)
 - [Discrete Critic Regularized Regression (CRR-Discrete)](https://arxiv.org/pdf/2006.15134.pdf)
diff --git a/docs/api/tianshou.policy.rst b/docs/api/tianshou.policy.rst
index fe129d8ec..6acd1d54b 100644
--- a/docs/api/tianshou.policy.rst
+++ b/docs/api/tianshou.policy.rst
@@ -129,6 +129,11 @@ Imitation
    :undoc-members:
    :show-inheritance:
 
+.. autoclass:: tianshou.policy.TD3BCPolicy
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
 .. autoclass:: tianshou.policy.DiscreteBCQPolicy
    :members:
    :undoc-members:
diff --git a/docs/index.rst b/docs/index.rst
index c18782718..7fce12f6b 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -31,6 +31,7 @@ Welcome to Tianshou!
 * :class:`~tianshou.policy.ImitationPolicy` Imitation Learning
 * :class:`~tianshou.policy.BCQPolicy` `Batch-Constrained deep Q-Learning <https://arxiv.org/pdf/1812.02900.pdf>`_
 * :class:`~tianshou.policy.CQLPolicy` `Conservative Q-Learning <https://arxiv.org/pdf/2006.04779.pdf>`_
+* :class:`~tianshou.policy.TD3BCPolicy` `Twin Delayed DDPG with Behavior Cloning <https://arxiv.org/pdf/2106.06860.pdf>`_
 * :class:`~tianshou.policy.DiscreteBCQPolicy` `Discrete Batch-Constrained deep Q-Learning <https://arxiv.org/pdf/1910.01708.pdf>`_
 * :class:`~tianshou.policy.DiscreteCQLPolicy` `Discrete Conservative Q-Learning <https://arxiv.org/pdf/2006.04779.pdf>`_
 * :class:`~tianshou.policy.DiscreteCRRPolicy` `Critic Regularized Regression <https://arxiv.org/pdf/2006.15134.pdf>`_
diff --git a/examples/offline/README.md b/examples/offline/README.md
index 61052c7c6..f52fb918c 100644
--- a/examples/offline/README.md
+++ b/examples/offline/README.md
@@ -35,6 +35,24 @@ Tianshou provides an `offline_trainer` for offline reinforcement learning. You c
 | HalfCheetah-v2        | halfcheetah-expert-v2 | 2864.37         | `python3 d4rl_cql.py --task HalfCheetah-v2 --expert-data-task halfcheetah-expert-v2` |
 | HalfCheetah-v2        | halfcheetah-medium-v2 | 6505.41         | `python3 d4rl_cql.py --task HalfCheetah-v2 --expert-data-task halfcheetah-medium-v2` |
 
+### TD3+BC
+
+| Environment           | Dataset               | CQL             | Parameters                                               |
+| --------------------- | --------------------- | --------------- | -------------------------------------------------------- |
+| HalfCheetah-v2        | halfcheetah-expert-v2 | 11788.25         | `python3 d4rl_td3_bc.py --task HalfCheetah-v2 --expert-data-task halfcheetah-expert-v2` |
+| HalfCheetah-v2        | halfcheetah-medium-v2 | 5741.13         | `python3 d4rl_td3_bc.py --task HalfCheetah-v2 --expert-data-task halfcheetah-medium-v2` |
+
+#### Observation normalization
+
+Following the original paper, we use observation normalization by default. You can turn it off by setting `--norm-obs 0`. The difference are small but consistent.
+
+| Dataset | w/ norm-obs | w/o norm-obs |
+| :--- | :--- | :--- |
+| halfcheeta-medium-v2 | 5741.13 | 5724.41 |
+| halfcheeta-expert-v2 | 11788.25 | 11665.77 |
+| walker2d-medium-v2 | 4051.76 | 3985.59 |
+| walker2d-expert-v2 | 5068.15 | 5027.75 |
+
 ## Discrete control
 
 For discrete control, we currently use ad hoc Atari data generated from a trained QRDQN agent.
diff --git a/examples/offline/d4rl_td3_bc.py b/examples/offline/d4rl_td3_bc.py
new file mode 100644
index 000000000..43ee21b31
--- /dev/null
+++ b/examples/offline/d4rl_td3_bc.py
@@ -0,0 +1,227 @@
+#!/usr/bin/env python3
+
+import argparse
+import datetime
+import os
+import pprint
+
+import gym
+import numpy as np
+import torch
+from torch.utils.tensorboard import SummaryWriter
+
+from examples.offline.utils import load_buffer_d4rl, normalize_all_obs_in_replay_buffer
+from tianshou.data import Collector
+from tianshou.env import SubprocVectorEnv, VectorEnvNormObs
+from tianshou.exploration import GaussianNoise
+from tianshou.policy import TD3BCPolicy
+from tianshou.trainer import offline_trainer
+from tianshou.utils import TensorboardLogger, WandbLogger
+from tianshou.utils.net.common import Net
+from tianshou.utils.net.continuous import Actor, Critic
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--task", type=str, default="HalfCheetah-v2")
+    parser.add_argument("--seed", type=int, default=0)
+    parser.add_argument(
+        "--expert-data-task", type=str, default="halfcheetah-expert-v2"
+    )
+    parser.add_argument("--buffer-size", type=int, default=1000000)
+    parser.add_argument("--hidden-sizes", type=int, nargs="*", default=[256, 256])
+    parser.add_argument("--actor-lr", type=float, default=3e-4)
+    parser.add_argument("--critic-lr", type=float, default=3e-4)
+    parser.add_argument("--epoch", type=int, default=200)
+    parser.add_argument("--step-per-epoch", type=int, default=5000)
+    parser.add_argument("--n-step", type=int, default=3)
+    parser.add_argument("--batch-size", type=int, default=256)
+
+    parser.add_argument("--alpha", type=float, default=2.5)
+    parser.add_argument("--exploration-noise", type=float, default=0.1)
+    parser.add_argument("--policy-noise", type=float, default=0.2)
+    parser.add_argument("--noise-clip", type=float, default=0.5)
+    parser.add_argument("--update-actor-freq", type=int, default=2)
+    parser.add_argument("--tau", type=float, default=0.005)
+    parser.add_argument("--gamma", type=float, default=0.99)
+    parser.add_argument("--norm-obs", type=int, default=1)
+
+    parser.add_argument("--eval-freq", type=int, default=1)
+    parser.add_argument("--test-num", type=int, default=10)
+    parser.add_argument("--logdir", type=str, default="log")
+    parser.add_argument("--render", type=float, default=1 / 35)
+    parser.add_argument(
+        "--device", type=str, default="cuda" if torch.cuda.is_available() else "cpu"
+    )
+    parser.add_argument("--resume-path", type=str, default=None)
+    parser.add_argument("--resume-id", type=str, default=None)
+    parser.add_argument(
+        "--logger",
+        type=str,
+        default="tensorboard",
+        choices=["tensorboard", "wandb"],
+    )
+    parser.add_argument("--wandb-project", type=str, default="offline_d4rl.benchmark")
+    parser.add_argument(
+        "--watch",
+        default=False,
+        action="store_true",
+        help="watch the play of pre-trained policy only",
+    )
+    return parser.parse_args()
+
+
+def test_td3_bc():
+    args = get_args()
+    env = gym.make(args.task)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    args.max_action = env.action_space.high[0]  # float
+    print("device:", args.device)
+    print("Observations shape:", args.state_shape)
+    print("Actions shape:", args.action_shape)
+    print("Action range:", np.min(env.action_space.low), np.max(env.action_space.high))
+
+    args.state_dim = args.state_shape[0]
+    args.action_dim = args.action_shape[0]
+    print("Max_action", args.max_action)
+
+    test_envs = SubprocVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.test_num)]
+    )
+    if args.norm_obs:
+        test_envs = VectorEnvNormObs(test_envs, update_obs_rms=False)
+
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    test_envs.seed(args.seed)
+
+    # model
+    # actor network
+    net_a = Net(
+        args.state_shape,
+        hidden_sizes=args.hidden_sizes,
+        device=args.device,
+    )
+    actor = Actor(
+        net_a,
+        action_shape=args.action_shape,
+        max_action=args.max_action,
+        device=args.device,
+    ).to(args.device)
+    actor_optim = torch.optim.Adam(actor.parameters(), lr=args.actor_lr)
+
+    # critic network
+    net_c1 = Net(
+        args.state_shape,
+        args.action_shape,
+        hidden_sizes=args.hidden_sizes,
+        concat=True,
+        device=args.device,
+    )
+    net_c2 = Net(
+        args.state_shape,
+        args.action_shape,
+        hidden_sizes=args.hidden_sizes,
+        concat=True,
+        device=args.device,
+    )
+    critic1 = Critic(net_c1, device=args.device).to(args.device)
+    critic1_optim = torch.optim.Adam(critic1.parameters(), lr=args.critic_lr)
+    critic2 = Critic(net_c2, device=args.device).to(args.device)
+    critic2_optim = torch.optim.Adam(critic2.parameters(), lr=args.critic_lr)
+
+    policy = TD3BCPolicy(
+        actor,
+        actor_optim,
+        critic1,
+        critic1_optim,
+        critic2,
+        critic2_optim,
+        tau=args.tau,
+        gamma=args.gamma,
+        exploration_noise=GaussianNoise(sigma=args.exploration_noise),
+        policy_noise=args.policy_noise,
+        update_actor_freq=args.update_actor_freq,
+        noise_clip=args.noise_clip,
+        alpha=args.alpha,
+        estimation_step=args.n_step,
+        action_space=env.action_space,
+    )
+
+    # load a previous policy
+    if args.resume_path:
+        policy.load_state_dict(torch.load(args.resume_path, map_location=args.device))
+        print("Loaded agent from: ", args.resume_path)
+
+    # collector
+    test_collector = Collector(policy, test_envs)
+
+    # log
+    now = datetime.datetime.now().strftime("%y%m%d-%H%M%S")
+    args.algo_name = "td3_bc"
+    log_name = os.path.join(args.task, args.algo_name, str(args.seed), now)
+    log_path = os.path.join(args.logdir, log_name)
+
+    # logger
+    if args.logger == "wandb":
+        logger = WandbLogger(
+            save_interval=1,
+            name=log_name.replace(os.path.sep, "__"),
+            run_id=args.resume_id,
+            config=args,
+            project=args.wandb_project,
+        )
+    writer = SummaryWriter(log_path)
+    writer.add_text("args", str(args))
+    if args.logger == "tensorboard":
+        logger = TensorboardLogger(writer)
+    else:  # wandb
+        logger.load(writer)
+
+    def save_best_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, "policy.pth"))
+
+    def watch():
+        if args.resume_path is None:
+            args.resume_path = os.path.join(log_path, "policy.pth")
+
+        policy.load_state_dict(
+            torch.load(args.resume_path, map_location=torch.device("cpu"))
+        )
+        policy.eval()
+        collector = Collector(policy, env)
+        collector.collect(n_episode=1, render=1 / 35)
+
+    if not args.watch:
+        replay_buffer = load_buffer_d4rl(args.expert_data_task)
+        if args.norm_obs:
+            replay_buffer, obs_rms = normalize_all_obs_in_replay_buffer(replay_buffer)
+            test_envs.set_obs_rms(obs_rms)
+        # trainer
+        result = offline_trainer(
+            policy,
+            replay_buffer,
+            test_collector,
+            args.epoch,
+            args.step_per_epoch,
+            args.test_num,
+            args.batch_size,
+            save_best_fn=save_best_fn,
+            logger=logger,
+        )
+        pprint.pprint(result)
+    else:
+        watch()
+
+    # Let's watch its performance!
+    policy.eval()
+    test_envs.seed(args.seed)
+    test_collector.reset()
+    result = test_collector.collect(n_episode=args.test_num, render=args.render)
+    print(f"Final reward: {result['rews'].mean()}, length: {result['lens'].mean()}")
+
+
+if __name__ == "__main__":
+    test_td3_bc()
diff --git a/examples/offline/utils.py b/examples/offline/utils.py
index 757baf69a..c6052795c 100644
--- a/examples/offline/utils.py
+++ b/examples/offline/utils.py
@@ -1,8 +1,12 @@
+from typing import Tuple
+
 import d4rl
 import gym
 import h5py
+import numpy as np
 
 from tianshou.data import ReplayBuffer
+from tianshou.utils import RunningMeanStd
 
 
 def load_buffer_d4rl(expert_data_task: str) -> ReplayBuffer:
@@ -27,3 +31,18 @@ def load_buffer(buffer_path: str) -> ReplayBuffer:
             obs_next=dataset["next_observations"]
         )
     return buffer
+
+
+def normalize_all_obs_in_replay_buffer(
+    replay_buffer: ReplayBuffer
+) -> Tuple[ReplayBuffer, RunningMeanStd]:
+    # compute obs mean and var
+    obs_rms = RunningMeanStd()
+    obs_rms.update(replay_buffer.obs)
+    _eps = np.finfo(np.float32).eps.item()
+    # normalize obs
+    replay_buffer._meta["obs"] = (replay_buffer.obs -
+                                  obs_rms.mean) / np.sqrt(obs_rms.var + _eps)
+    replay_buffer._meta["obs_next"] = (replay_buffer.obs_next -
+                                       obs_rms.mean) / np.sqrt(obs_rms.var + _eps)
+    return replay_buffer, obs_rms
diff --git a/test/offline/test_td3_bc.py b/test/offline/test_td3_bc.py
new file mode 100644
index 000000000..e34dfc6d2
--- /dev/null
+++ b/test/offline/test_td3_bc.py
@@ -0,0 +1,215 @@
+import argparse
+import datetime
+import os
+import pickle
+import pprint
+
+import gym
+import numpy as np
+import torch
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.data import Collector, VectorReplayBuffer
+from tianshou.env import DummyVectorEnv
+from tianshou.exploration import GaussianNoise
+from tianshou.policy import TD3BCPolicy
+from tianshou.trainer import OfflineTrainer
+from tianshou.utils import TensorboardLogger
+from tianshou.utils.net.common import Net
+from tianshou.utils.net.continuous import Actor, Critic
+
+if __name__ == "__main__":
+    from gather_pendulum_data import expert_file_name, gather_data
+else:  # pytest
+    from test.offline.gather_pendulum_data import expert_file_name, gather_data
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--task', type=str, default='Pendulum-v1')
+    parser.add_argument('--reward-threshold', type=float, default=None)
+    parser.add_argument('--seed', type=int, default=0)
+    parser.add_argument('--hidden-sizes', type=int, nargs='*', default=[64, 64])
+    parser.add_argument('--actor-lr', type=float, default=1e-3)
+    parser.add_argument('--critic-lr', type=float, default=1e-3)
+    parser.add_argument('--epoch', type=int, default=5)
+    parser.add_argument('--step-per-epoch', type=int, default=500)
+    parser.add_argument('--n-step', type=int, default=3)
+    parser.add_argument('--batch-size', type=int, default=64)
+    parser.add_argument('--alpha', type=float, default=2.5)
+    parser.add_argument("--exploration-noise", type=float, default=0.1)
+    parser.add_argument("--policy-noise", type=float, default=0.2)
+    parser.add_argument("--noise-clip", type=float, default=0.5)
+    parser.add_argument("--update-actor-freq", type=int, default=2)
+    parser.add_argument("--tau", type=float, default=0.005)
+    parser.add_argument("--gamma", type=float, default=0.99)
+
+    parser.add_argument("--eval-freq", type=int, default=1)
+    parser.add_argument('--test-num', type=int, default=10)
+    parser.add_argument('--logdir', type=str, default='log')
+    parser.add_argument('--render', type=float, default=1 / 35)
+    parser.add_argument(
+        '--device', type=str, default='cuda' if torch.cuda.is_available() else 'cpu'
+    )
+    parser.add_argument('--resume-path', type=str, default=None)
+    parser.add_argument(
+        '--watch',
+        default=False,
+        action='store_true',
+        help='watch the play of pre-trained policy only',
+    )
+    parser.add_argument("--load-buffer-name", type=str, default=expert_file_name())
+    args = parser.parse_known_args()[0]
+    return args
+
+
+def test_td3_bc(args=get_args()):
+    if os.path.exists(args.load_buffer_name) and os.path.isfile(args.load_buffer_name):
+        if args.load_buffer_name.endswith(".hdf5"):
+            buffer = VectorReplayBuffer.load_hdf5(args.load_buffer_name)
+        else:
+            buffer = pickle.load(open(args.load_buffer_name, "rb"))
+    else:
+        buffer = gather_data()
+    env = gym.make(args.task)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    args.max_action = env.action_space.high[0]  # float
+    if args.reward_threshold is None:
+        # too low?
+        default_reward_threshold = {"Pendulum-v0": -1200, "Pendulum-v1": -1200}
+        args.reward_threshold = default_reward_threshold.get(
+            args.task, env.spec.reward_threshold
+        )
+
+    args.state_dim = args.state_shape[0]
+    args.action_dim = args.action_shape[0]
+    # test_envs = gym.make(args.task)
+    test_envs = DummyVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.test_num)]
+    )
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    test_envs.seed(args.seed)
+
+    # model
+    # actor network
+    net_a = Net(
+        args.state_shape,
+        hidden_sizes=args.hidden_sizes,
+        device=args.device,
+    )
+    actor = Actor(
+        net_a,
+        action_shape=args.action_shape,
+        max_action=args.max_action,
+        device=args.device,
+    ).to(args.device)
+    actor_optim = torch.optim.Adam(actor.parameters(), lr=args.actor_lr)
+
+    # critic network
+    net_c1 = Net(
+        args.state_shape,
+        args.action_shape,
+        hidden_sizes=args.hidden_sizes,
+        concat=True,
+        device=args.device,
+    )
+    net_c2 = Net(
+        args.state_shape,
+        args.action_shape,
+        hidden_sizes=args.hidden_sizes,
+        concat=True,
+        device=args.device,
+    )
+    critic1 = Critic(net_c1, device=args.device).to(args.device)
+    critic1_optim = torch.optim.Adam(critic1.parameters(), lr=args.critic_lr)
+    critic2 = Critic(net_c2, device=args.device).to(args.device)
+    critic2_optim = torch.optim.Adam(critic2.parameters(), lr=args.critic_lr)
+
+    policy = TD3BCPolicy(
+        actor,
+        actor_optim,
+        critic1,
+        critic1_optim,
+        critic2,
+        critic2_optim,
+        tau=args.tau,
+        gamma=args.gamma,
+        exploration_noise=GaussianNoise(sigma=args.exploration_noise),
+        policy_noise=args.policy_noise,
+        update_actor_freq=args.update_actor_freq,
+        noise_clip=args.noise_clip,
+        alpha=args.alpha,
+        estimation_step=args.n_step,
+        action_space=env.action_space,
+    )
+
+    # load a previous policy
+    if args.resume_path:
+        policy.load_state_dict(torch.load(args.resume_path, map_location=args.device))
+        print("Loaded agent from: ", args.resume_path)
+
+    # collector
+    # buffer has been gathered
+    # train_collector = Collector(policy, train_envs, buffer, exploration_noise=True)
+    test_collector = Collector(policy, test_envs)
+    # log
+    t0 = datetime.datetime.now().strftime("%m%d_%H%M%S")
+    log_file = f'seed_{args.seed}_{t0}-{args.task.replace("-", "_")}_td3_bc'
+    log_path = os.path.join(args.logdir, args.task, 'td3_bc', log_file)
+    writer = SummaryWriter(log_path)
+    writer.add_text("args", str(args))
+    logger = TensorboardLogger(writer)
+
+    def save_best_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        return mean_rewards >= args.reward_threshold
+
+    def watch():
+        policy.load_state_dict(
+            torch.load(
+                os.path.join(log_path, 'policy.pth'), map_location=torch.device('cpu')
+            )
+        )
+        policy.eval()
+        collector = Collector(policy, env)
+        collector.collect(n_episode=1, render=1 / 35)
+
+    # trainer
+    trainer = OfflineTrainer(
+        policy,
+        buffer,
+        test_collector,
+        args.epoch,
+        args.step_per_epoch,
+        args.test_num,
+        args.batch_size,
+        save_best_fn=save_best_fn,
+        stop_fn=stop_fn,
+        logger=logger,
+    )
+
+    for epoch, epoch_stat, info in trainer:
+        print(f"Epoch: {epoch}")
+        print(epoch_stat)
+        print(info)
+
+    assert stop_fn(info["best_reward"])
+
+    # Let's watch its performance!
+    if __name__ == "__main__":
+        pprint.pprint(info)
+        env = gym.make(args.task)
+        policy.eval()
+        collector = Collector(policy, env)
+        result = collector.collect(n_episode=1, render=args.render)
+        rews, lens = result["rews"], result["lens"]
+        print(f"Final reward: {rews.mean()}, length: {lens.mean()}")
+
+
+if __name__ == '__main__':
+    test_td3_bc()
diff --git a/tianshou/policy/__init__.py b/tianshou/policy/__init__.py
index 8007bad9c..c8fa45e8e 100644
--- a/tianshou/policy/__init__.py
+++ b/tianshou/policy/__init__.py
@@ -23,6 +23,7 @@
 from tianshou.policy.imitation.base import ImitationPolicy
 from tianshou.policy.imitation.bcq import BCQPolicy
 from tianshou.policy.imitation.cql import CQLPolicy
+from tianshou.policy.imitation.td3_bc import TD3BCPolicy
 from tianshou.policy.imitation.discrete_bcq import DiscreteBCQPolicy
 from tianshou.policy.imitation.discrete_cql import DiscreteCQLPolicy
 from tianshou.policy.imitation.discrete_crr import DiscreteCRRPolicy
@@ -54,6 +55,7 @@
     "ImitationPolicy",
     "BCQPolicy",
     "CQLPolicy",
+    "TD3BCPolicy",
     "DiscreteBCQPolicy",
     "DiscreteCQLPolicy",
     "DiscreteCRRPolicy",
diff --git a/tianshou/policy/imitation/td3_bc.py b/tianshou/policy/imitation/td3_bc.py
new file mode 100644
index 000000000..9746659ad
--- /dev/null
+++ b/tianshou/policy/imitation/td3_bc.py
@@ -0,0 +1,107 @@
+from typing import Any, Dict, Optional
+
+import torch
+import torch.nn.functional as F
+
+from tianshou.data import Batch, to_torch_as
+from tianshou.exploration import BaseNoise, GaussianNoise
+from tianshou.policy import TD3Policy
+
+
+class TD3BCPolicy(TD3Policy):
+    """Implementation of TD3+BC. arXiv:2106.06860.
+
+    :param torch.nn.Module actor: the actor network following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> logits)
+    :param torch.optim.Optimizer actor_optim: the optimizer for actor network.
+    :param torch.nn.Module critic1: the first critic network. (s, a -> Q(s, a))
+    :param torch.optim.Optimizer critic1_optim: the optimizer for the first
+        critic network.
+    :param torch.nn.Module critic2: the second critic network. (s, a -> Q(s, a))
+    :param torch.optim.Optimizer critic2_optim: the optimizer for the second
+        critic network.
+    :param float tau: param for soft update of the target network. Default to 0.005.
+    :param float gamma: discount factor, in [0, 1]. Default to 0.99.
+    :param float exploration_noise: the exploration noise, add to the action.
+        Default to ``GaussianNoise(sigma=0.1)``
+    :param float policy_noise: the noise used in updating policy network.
+        Default to 0.2.
+    :param int update_actor_freq: the update frequency of actor network.
+        Default to 2.
+    :param float noise_clip: the clipping range used in updating policy network.
+        Default to 0.5.
+    :param float alpha: the value of alpha, which controls the weight for TD3 learning
+        relative to behavior cloning.
+    :param bool reward_normalization: normalize the reward to Normal(0, 1).
+        Default to False.
+    :param bool action_scaling: whether to map actions from range [-1, 1] to range
+        [action_spaces.low, action_spaces.high]. Default to True.
+    :param str action_bound_method: method to bound action to range [-1, 1], can be
+        either "clip" (for simply clipping the action) or empty string for no bounding.
+        Default to "clip".
+    :param Optional[gym.Space] action_space: env's action space, mandatory if you want
+        to use option "action_scaling" or "action_bound_method". Default to None.
+    :param lr_scheduler: a learning rate scheduler that adjusts the learning rate in
+        optimizer in each policy.update(). Default to None (no lr_scheduler).
+
+    .. seealso::
+
+        Please refer to :class:`~tianshou.policy.BasePolicy` for more detailed
+        explanation.
+    """
+
+    def __init__(
+        self,
+        actor: torch.nn.Module,
+        actor_optim: torch.optim.Optimizer,
+        critic1: torch.nn.Module,
+        critic1_optim: torch.optim.Optimizer,
+        critic2: torch.nn.Module,
+        critic2_optim: torch.optim.Optimizer,
+        tau: float = 0.005,
+        gamma: float = 0.99,
+        exploration_noise: Optional[BaseNoise] = GaussianNoise(sigma=0.1),
+        policy_noise: float = 0.2,
+        update_actor_freq: int = 2,
+        noise_clip: float = 0.5,
+        alpha: float = 2.5,
+        reward_normalization: bool = False,
+        estimation_step: int = 1,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(
+            actor, actor_optim, critic1, critic1_optim, critic2, critic2_optim, tau,
+            gamma, exploration_noise, policy_noise, update_actor_freq, noise_clip,
+            reward_normalization, estimation_step, **kwargs
+        )
+        self._alpha = alpha
+
+    def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
+        # critic 1&2
+        td1, critic1_loss = self._mse_optimizer(
+            batch, self.critic1, self.critic1_optim
+        )
+        td2, critic2_loss = self._mse_optimizer(
+            batch, self.critic2, self.critic2_optim
+        )
+        batch.weight = (td1 + td2) / 2.0  # prio-buffer
+
+        # actor
+        if self._cnt % self._freq == 0:
+            act = self(batch, eps=0.0).act
+            q_value = self.critic1(batch.obs, act)
+            lmbda = self._alpha / q_value.abs().mean().detach()
+            actor_loss = -lmbda * q_value.mean() + F.mse_loss(
+                act, to_torch_as(batch.act, act)
+            )
+            self.actor_optim.zero_grad()
+            actor_loss.backward()
+            self._last = actor_loss.item()
+            self.actor_optim.step()
+            self.sync_weight()
+        self._cnt += 1
+        return {
+            "loss/actor": self._last,
+            "loss/critic1": critic1_loss.item(),
+            "loss/critic2": critic2_loss.item(),
+        }
diff --git a/tianshou/trainer/base.py b/tianshou/trainer/base.py
index b4dcfb6be..aa3d1fc77 100644
--- a/tianshou/trainer/base.py
+++ b/tianshou/trainer/base.py
@@ -301,6 +301,10 @@ def __next__(self) -> Union[None, Tuple[int, Dict[str, Any], Dict[str, Any]]]:
             if t.n <= t.total and not self.stop_fn_flag:
                 t.update()
 
+        # for offline RL
+        if self.train_collector is None:
+            self.env_step = self.gradient_step * self.batch_size
+
         if not self.stop_fn_flag:
             self.logger.save_data(
                 self.epoch, self.env_step, self.gradient_step, self.save_checkpoint_fn